Hi Susan,
It's my understanding that DataCare would be looking for exclusive access to your Adagio dataset during the backup and data check. That depends on whether the option is checked on the job, 'require exclusive access'. Do your DC jobs require exclusive access? Even without exclusive access, the job should have flagged it as an error. I don't think the creation of these .Z## files are typical. The backup procedure can normally detect when a file is open by some user.